The influence of boundary conditions on dispersion in an elastic plate

The propagation of waves along an elastic layer of uniform thickness has been an area of active research for many years. Many contributions have been made to the study of small amplitude wave propagation in a linear isotropic elastic layer, almost all in respect of traction-free boundary conditions. In this paper the associated dispersion relation is briefly reviewed. We also consider two other non-classical types of the boundary conditions, the so-called fixed and free-fixed problems. The associated dispersion relations are first investigated numerically, from which it is shown that no analogues of classical bending or extension exists. The fixed-free case is of particular interest as, unlike the other two cases, it does not decompose into symmetric and anti-symmetric parts. A representation of the associated dispersion relation is established in terms of the fixed and free dispersion relations. Long wave approximations of the phase are obtained; it is envisaged that these approximations will allow future establishment of appropriate long wave models.